### Some articles on *partial orders, order, partial order*:

Order Dimension Two

... The

... The

**partial orders**with**order**dimension two may be characterized as the**partial orders**whose comparability graph is the complement of the comparability graph of a different ... That is, P is a**partial order**with**order**dimension two if and only if there exists a**partial order**Q on the same set of elements, such that every pair x, y of distinct elements is comparable in ... If P is realized by two linear extensions, then**partial order**Q complementary to P may be realized by reversing one of the two linear extensions ...Birkhoff's Representation Theorem - Functoriality

... as stated above, is a correspondence between individual

... as stated above, is a correspondence between individual

**partial orders**and distributive lattices ... However, it can also be extended to a correspondence between**order**-preserving functions of**partial orders**and bounded homomorphisms of the ... Let 2 denote the**partial order**on the two-element set {0, 1}, with the**order**relation 0 < 1, and (following Stanley) let J(P) denote the distributive ...Coxeter Group -

... Using reduced words one may define three

**Partial Orders**... Using reduced words one may define three

**partial orders**on the Coxeter group, the (right) weak**order**, the absolute**order**and the Bruhat**order**(named ... An element v exceeds an element u in the Bruhat**order**if some (or equivalently, any) reduced word for v contains a reduced word for u as a substring, where some ... In the weak**order**, v ≥ u if some reduced word for v contains a reduced word for u as an initial segment ...Linear Extension - Related Results

... The algorithmic problem of constructing a linear extension of a

... The algorithmic problem of constructing a linear extension of a

**partial order**on a finite set, represented by a directed acyclic graph with the set's elements as its vertices, is known as topological sorting ... extension, the problem of counting all linear extensions of a finite**partial order**is #P-complete however, it may be estimated by a fully polynomial-time randomized approximation scheme ... Among all**partial orders**with a fixed number of elements and a fixed number of comparable pairs, the**partial orders**that have the largest number of linear extensions are semiorders ...### Famous quotes containing the words orders and/or partial:

“The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense quantum sufficit, add a little application to the rules and *orders* of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”

—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)

“America is hard to see.

Less *partial* witnesses than he

In book on book have testified

They could not see it from outside....”

—Robert Frost (1874–1963)

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